Math Tools
Binary Calculator
Convert binary to decimal, decimal to binary, and perform binary arithmetic with formulas, examples, and quick reference tables.
Binary Calculator
Convert binary to decimal, decimal to binary, and perform binary addition and binary subtraction.
Convert a binary number into its decimal value.
Result
10
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What this binary calculator does
This binary calculator converts between binary and decimal and can also solve binary addition and binary subtraction problems.
What is a binary calculator?
A binary calculator is a tool that helps you work with binary numbers, which use only the digits 0 and 1. Instead of solving conversions and arithmetic by hand, you can enter your values and instantly get accurate results.
This is useful for students, programmers, computer science learners, electronics work, digital logic practice, and anyone who needs to convert binary to decimal, decimal to binary, or perform binary addition and subtraction quickly.
Binary to decimal and decimal to binary formulas
Binary to decimal
Multiply each binary digit by its power of 2 place value, then add the results.
Example: 1010 = 1×8 + 0×4 + 1×2 + 0×1 = 10
Decimal to binary
Repeatedly divide the decimal number by 2 and read the remainders from bottom to top.
Example: 10 = 1010
Examples for binary to decimal
These worked examples show common binary conversions and binary arithmetic results.
| Example | Result |
|---|---|
| 1010 | 10 |
| 1111 | 15 |
| 100000 | 32 |
Binary place value table
Binary numbers are based on powers of 2. Each position has a place value that doubles as you move left.
| Binary place | Decimal value |
|---|---|
| 2⁷ | 128 |
| 2⁶ | 64 |
| 2⁵ | 32 |
| 2⁴ | 16 |
| 2³ | 8 |
| 2² | 4 |
| 2¹ | 2 |
| 2⁰ | 1 |
Binary to decimal table
This quick binary to decimal chart is useful for checking common values and learning how binary numbers map to decimal numbers.
| Binary | Decimal |
|---|---|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
How binary addition and binary subtraction work
Binary addition follows simple rules: 0 + 0 = 0, 0 + 1 = 1, and 1 + 1 = 10. When the sum is 10, you write 0 and carry 1 to the next column.
Binary subtraction also works column by column. If you subtract 1 from 0, you need to borrow from the next place value, just like in decimal subtraction. A binary calculator helps you avoid mistakes when carrying or borrowing across multiple digits.
Where binary numbers are used
Binary numbers are used in computers, digital electronics, logic circuits, memory systems, machine-level processing, and data storage. Since computers operate using two states, binary is the basic language behind modern computing.
Learning binary math helps students understand how digital systems work, while developers and engineers often use binary for debugging, bitwise operations, and low-level technical tasks.
Binary calculator FAQ and common binary conversion questions
How do you convert binary to decimal?
Multiply each binary digit by its power of 2 place value and add the results together. For example, 1010 in binary equals 10 in decimal.
How do you convert decimal to binary?
Divide the decimal number by 2 repeatedly and track the remainders. Reading those remainders from bottom to top gives the binary form.
What is binary addition?
Binary addition is adding numbers made only of 0s and 1s using carry rules. For example, 1 + 1 equals 10 in binary.
What is binary subtraction?
Binary subtraction subtracts one binary number from another using borrowing rules when needed, similar to decimal subtraction.
Why is binary important in computing?
Binary is important because computers and digital systems work with two-state logic, commonly represented as 0 and 1.
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